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Practical Considerations

While the digital mass simulator has the desirable properties of the bilinear transform, it is also not perfect from a practical point of view: (1) There is a pole at half the sampling rate ($ z=-1$ ). (2) There is a delay-free path from input to output.

The first problem can easily be circumvented by introducing a loss factor $ g$ , moving the pole from $ z=-1$ to $ z=-g$ , where $ g\in[0,1)$ and $ g\approx1$ . This is sometimes called the ``leaky integrator''.

The second problem arises when making loops of elements (e.g., a mass-spring chain which forms a loop). Since the individual elements have no delay from input to output, a loop of elements is not computable using standard signal processing methods. The solution proposed by Alfred Fettweis is known as ``wave digital filters,'' a topic taken up in §F.1.

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2017-02-20 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University